WASHINGTON
— When it came to foreign policy, the hallmark of the first term of George W. Bush was "accept no limits, and go it alone."

Now President Bush is making it clear that in his second term he wants to work more closely with the world and with multilateral institutions.

The question is how he plans to do that. Skepticism toward global collective action remains high in the administration, while much of the world is still estranged from the United States after the war in Iraq. At the same time, critical voices on the president's right are multiplying against the United Nations and other international bodies. "It's going to be one of the key story lines of the second term, how the president manages to engage the world and work with the international system, especially when much of that system doesn't work very well," says John Hulsman, an expert in transatlantic relations at the Heritage Foundation in Washington.

One change will be the president simply engaging foreign leaders more and upping the emphasis on dialogue. The White House last week announced that Bush will make the first trip of his second term to Europe: In February he'll travel to Brussels to meet with NATO leaders. Also in Brussels, Bush will meet with leaders of the European Union.

The White House says other stops are yet to be announced. Bush is expected to visit Germany, where he will continue patching relations with German Chancellor Gerhard Schröder. He could also visit US troops stationed there.

The high profile the White House is giving the Europe trip suggests that Bush will emphasize multilateral institutions he considers capable of taking necessary action - including the North Atlantic Alliance. NATO has recently agreed to participate in training Iraq's fledgling security forces. But even there Bush is not encountering smooth sailing. If he wants support in areas like Iraq, he will have to listen to opposing views - and accommodate differing positions, some experts say.

At a recent meeting of NATO ministers, a half-dozen member countries - including Germany, France, and Spain - continued to refuse to send any military personnel to Iraq. The countries say that trainers in Iraq would require many times their number in protective troops, and that training can be better undertaken outside Iraq.

In Washington, French Ambassador Jean-David Levitte notes that France has offered to train a new Iraqi "gendarmerie," or military police force - either in France or in a third country - but it is still awaiting a decision from Iraqi Interim Prime Minister Iyad Allawi.

There are other signs that foreign governments are picking up on a new, more internationalist tone from the White House - and are focusing on how to work with it.

"We are at a point where we are making a new start," says John Bruton, the European Union's new ambassador in Washington.

In a conversation last week with a small group of journalists, Ambassador Levitte said that "despite lingering resentment" over opposition to the war in Iraq, he sensed "more and more positive feelings in the Bush II administration" and "a friendly hand extended to Europe." Saying France has learned that Bush is a president "interested in actions and results" more than "process," he said France and Europe are looking for the US to take steps on Iran and the Israeli-Palestinian peace process "that can lead to results."

Sources close to the administration say the president's desire to engage the world is more than postelection rhetorical flourish, as some have suggested. But they add that Bush is likely to proceed in ways that deemphasize those bodies the president considers least effective, particularly the UN. "The administration is now reaching out to a wide variety of countries. They are making sure those countries are in the loop, that they know what the US is contemplating, and that they have input to our thinking on foreign-policy matters, and that's an important change," says Danielle Pletka, a foreign-policy expert at the American Enterprise Institute in Washington.

"But you do not need a framework in which to work with your allies, and the idea that you need some Good Housekeeping seal of approval from the secretary-general of the UN or any other institution to proceed with a robust multilateralism is not right," says Ms. Pletka, who has close ties to the administration's strongest advocates of the use of American power.

Of course some observers expect the world to react cautiously to new Bush administration overtones and to "test them out." "You can't disregard the concerns and interests of the international community over an extended period of time, and then ask people to come in and help you the next day on what you want," says Jeswald Salacuse, an international-relations specialist at Tufts University's Fletcher School in Medford, Mass.

Others say that a clear signal of how Bush plans to approach the world will come from whom he appoints as ambassador to the UN - and how the administration responds to a recent UN panel on UN reforms for the 21st century.

"If he sends up a neoconservative type, who's opposed to international limits and skeptical of the UN's paper treaties, that would say more that the US wants to walk away or radically transform [the UN]," says Edward Luck, an expert in UN-US relations at Columbia University in New York.

Bush seems to consider himself a true friend of the UN, Mr. Luck says - but a friend who believes it must either become more effective or be irrelevant, he says.

If Bush prefers to ignore the UN, "then it could be someone bland, just to fill the post," Mr. Luck says. "Or it could be someone known as a strong supporter yet fairly critical.... I hope it's the latter," he adds, "because that would suggest that while they may keep the institution's feet to the fire, they really want to use it."